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x_1 + x_2 +...+ x_n = 16, 1/x_1 + 1/x_2 +...+ 1/x_n =1

Source: Singapore Junior Math Olympiad 2012 2nd Round p4 SMO

March 25, 2020

system of equationsalgebra

Problem Statement

Determine the values of the positive integer

n

for which the following system of equations has a solution in positive integers

x_1, x_2,...,, x_n

. Find all solutions for each such

n

\begin{cases} x_1 + x_2 +...+ x_n = 16 \\ \\ \dfrac{1}{x_1} + \dfrac{1}{x_2} +...+ \dfrac{1}{x_n} = 1\end{cases}